Genius Stuff with ujan
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<p style="text-align: left;">Problem 6 : answer is b by using common sense and visualization I think there is no need of explanation in this question. Pardon me if I am wrong .</p>
Problem 5 : we can take some multiples of 6 to find this answer .
6 _we have it's factors : 1*6 and 2*3 and hence we get two possible sums 7 and 5.
12 _ we have it's factors: 1*12, 2*6,3*4 and we get some other sums 8 and 7( as a dice can't show 12 we ain't gonna take that case)
18_ we have it's factors _ 1*18,2*9,3*6 and we get sums 9 only ( as a dice can't show 12 and 9 we aren't taking that case)
We see that we get all the options 5,7,8,9 but not 6 hence we get answer as 6 .
Logic 2 : if we break 6 into all possible groups of two numbers having sum 6 and multiply each of those cases, we will get a multiple of 6 in none of those cases . Hence the answer is 6 , again.
Problem 4 : first , we find the sum of numbers from 1 to 9 .
By using the arithmetic progression summation formula we get the sum of first n natural numbers as (n)(n+1)/2.
By putting 9(as there are 9 terms) in the same , we get 9*10/2=45.
Now we find the nearest perfect sq. LESS THAN 45 ( coz no sum from 1 to 9 can be greater than which we have taken as no number here is omitted and since our protagonist has missed a number from one to nine his sum is bound to less than 45 ).
We see that the number satisfying these conditions is 36 . Now we subtract: 45-36 =9 . So He must've missed 9 .
Problem 3: we can find the area of the larger squares ( the outline of gray regions) and from it the area of white square in it . By doing so we get : (7*7-4*4)+(10*10-9*9) = (49-16)+(100-81)=33+19=52